Evaluate the Integral from -pi/2 to pi of 20 * abs cos(x) dx ? I got the answer -20 but it seems to be incorrect. Can anyone provide an explanation?
I found out what I did wrong, the derivative of cos(x) = sin(x) and then sin (pi/2) = 1 and sin (-pi/2) = -1 so sin(pi/2) - sin (-pi/2) = 2 and 20*2 = 40 while the next term sin (pi) =0 and sin (pi/2) = 1 so 0-1 = -1 and 20*-1 = -20. After that, by subtracting the two terms, 40- (-20) = 60.
But how do you know where to split the integral?Are there any definitions as to how to split an abs( ) integral?
Plato and romsek split the integral at pi/2 since cos(x) crosses the x-axis there. So abs(cos(x)) = cos(x) before that and abs(cos(x)) = -cos(x) after that. That's typical for integrals of functions containing absolute values.
- Hollywood